The man was taken to San Francisco General Hospital for a mental and physical evaluation.
"After about six hours of negotiations, we were finally able to resolve this peacefully, and the subject eventually turned himself over," said Ofc. Carlos Manfredi, with the SFPD.
The first moments were tense as all of Civic Center was closed to pedestrian traffic, as were the nearby buildings including the library and the Asian Art Museum.
The incident was first reported by San Francisco Fire Department officials on Twitter around 12:25 p.m.
Police and fire officials initially evacuated the plaza and asked people to avoid the area. Police say the armed man called police just before noon and was threatening to use it.
"This person has a semi-automatic handgun. He has threatened to use the gun on officers and on himself," said San Francisco police officer Carlos Manfredi.
SWAT Team units and police negotiators are on scene trying to convince the man to surrender.
"He's using words that he may want to end his life or take out other people and we don't want that to happen," Manfredi said earlier on, as the negiations were on-going.
Hundreds of people live inside the evacuation zone, not knowing when they might be allowed to go home. Police say they are in no hurry to end the standoff and it could continue for several hours.
In the end, not a shot was fired. Officers decided to call in crisis negotiators, something they're doing more often.
"This is our 75th call out for our hostage negotiators for people in crisis. Last year it was 50," explained Manfredi.
The standoff ended at about 6 p.m. on Saturday evening and the concert began as scheduled.